VR is Vibration Reduction (Nikon term)
The both mean the same thing. Technology built into a lens or the camera senses camera movement and makes constant micro adjustments to compensate for that shake. It's a great technology that allows you to shoot hand held is situations that would result in blurry photos if you didn't have it.
If you have IS/VR turned on and your camera is not moving, such s when it is on a tripod, the IS/VR will actually introduce vibration trying to adjust for movement that is not there. Under most conditions you want to turn it off when mounting your camera on a tripod. Don't forget to turn it back on when you go back to shooting hand held or you will be disappointed when you look at your photos later. Some of the newer lenses can sense when there is no movement and turn the IS/VR off. None of mine do that so I have to rely on my memory, which is why I get more blurry photos than I should.
|5D Mark ii, 300mm, 1/40 second|
|5D Mark ii, 105mm, 1.3 seconds|
|5D Mark ii, 300mm, 1/8 second|
These are all shot with either a 300mm lens or a 24-105mm @ 105mm on a Canon 5D mark ii with IS turned on.
As with most things, there are exceptions to the rules. Don't assume that if you are following what you were told you will always get great results. It's important to be aware of conditions and make the appropriate adjustments to the rules.